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Two new permutation polynomials with the form \({\left(x^{2^k}+x+\delta\right)^{s}+x}\) over \({\mathbb{F}_{2^n}}\)

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Abstract

This note presents two new permutation polynomials with the form \({p(x)=\left(x^{2^k}+x+\delta\right)^{s}+x}\) over the finite field \({\mathbb{F}_{2^n}}\) as a supplement of the recent work of Yuan, Ding, Wang and Pieprzyk.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Hubei University, 430062, Wuhan, China

    Xiangyong Zeng & Xishun Zhu

  2. The State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, 100049, Beijing, China

    Xiangyong Zeng & Lei Hu

  3. The Key Laboratory of Mathematics Mechanization, Institute of System Sciences, AMSS, Chinese Academy of Sciences, 100190, Beijing, China

    Lei Hu

Authors
  1. Xiangyong Zeng
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  2. Xishun Zhu
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  3. Lei Hu
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Correspondence to Xiangyong Zeng.

Additional information

This work was partially supported by the National Natural Science Foundation of China under Grants 60973130, 60773134, 10990011, abnd National Basic Resarch (973) Program of China (2007CB311201). The work of X. Zeng was also supported by the Natural Science Foundation for Excellant Youth Scholars of Hubei Province of China (2009CDA147).

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Zeng, X., Zhu, X. & Hu, L. Two new permutation polynomials with the form \({\left(x^{2^k}+x+\delta\right)^{s}+x}\) over \({\mathbb{F}_{2^n}}\) . AAECC 21, 145–150 (2010). https://doi.org/10.1007/s00200-010-0120-6

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  • DOI: https://doi.org/10.1007/s00200-010-0120-6

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